Quantum Many Body Systems and Strongly Correlated Electrons II

Advanced course given by Massimo Capone, Michele Fabrizio

Term: 2

Start: 04-02-2019 End: 16-04-2019 Room: 131

Credits: 4

Schedule: Mon 11:00 - 13:00, Thu 11:00 - 13:00

Program

This is the second course of many-body physics. 

The course will explore the effect of interactions in a fermionic system, with a particular emphasis on lattice models (Hubbard models and related). 

The main topics are

- The phase diagram of the Hubbard model: reminder of the antiferromagnetic properties

- a short review of the Landau theory of normal Fermi liquids

- The Gutzwiller approximation

- Slave Particles: Slave Bosons and the Brinkman-Rice transition

- Slave Spins

- (maybe) Hubbard I and III approximations

- Dynamical Mean-Field Theory:

 

  • From historical methods to Dynamical Mean-Field Theory: A new view on the correlated electron problem
  • How to construct the DMFT: Cavity method
  • How to solve DMFT: self-consistency, mapping on impurity models and "impurity" solvers
  • The Mott-Hubbard transition in DMFT. Some analytical arguments
  • A numerical implementation of DMFT and the Mott transition
  • Multiorbital Mott transition: the Hund's coupling, spin-orbit coupling
  • Electron-phonon interaction